Give a primitive Pythagorean triple.

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Multiple Choice

Give a primitive Pythagorean triple.

Explanation:
A primitive Pythagorean triple is a trio of integers a, b, c that satisfies a^2 + b^2 = c^2 and has no common divisor greater than 1 among a, b, and c. In other words, the greatest common divisor of all three numbers is 1. For the set 3, 4, 5: 3^2 + 4^2 equals 9 + 16 = 25, which is 5^2, so it forms a Pythagorean triple. The gcd of 3, 4, and 5 is 1, so this triple is primitive. The other sets are multiples of 3, 4, 5 (2×, 3×, 4×). They satisfy the Pythagorean relation, but each has a common divisor greater than 1 (2, 3, and 4 respectively), so they are not primitive.

A primitive Pythagorean triple is a trio of integers a, b, c that satisfies a^2 + b^2 = c^2 and has no common divisor greater than 1 among a, b, and c. In other words, the greatest common divisor of all three numbers is 1.

For the set 3, 4, 5: 3^2 + 4^2 equals 9 + 16 = 25, which is 5^2, so it forms a Pythagorean triple. The gcd of 3, 4, and 5 is 1, so this triple is primitive.

The other sets are multiples of 3, 4, 5 (2×, 3×, 4×). They satisfy the Pythagorean relation, but each has a common divisor greater than 1 (2, 3, and 4 respectively), so they are not primitive.

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